Engineering Structures 46 (2013) 569–580

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Engineering Structures

journal homepage: www.elsevier .com/ locate /engstruct

Bridge rating protocol using ambient trucks through structural healthmonitoring system

0141-0296/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.08.012

⇑ Corresponding author.E-mail address: jseo@iastate.edu (J. Seo).

Junwon Seo a,⇑, Brent Phares b, Ping Lu c, Terry Wipf a, Justin Dahlberg b

a Department of Civil, Construction, and Environmental Engineering, Iowa State University, IA50011, United Statesb Bridge Engineering Center, Iowa State University, IA 50010,United Statesc Iowa Department of Transportation, IA 50010, United States

a r t i c l e i n f o

Article history:Received 1 November 2011Revised 15 August 2012Accepted 16 August 2012Available online 28 September 2012

Keywords:BridgeStructural capacityModel calibrationStructural health monitoring systemAmbient trucks

a b s t r a c t

A protocol for the development of a set of load rating distributions for a steel I-girder bridge will be pre-sented. The critical regions of the bridge were instrumented using strain sensors to measure the real-timestrain time history resulting from ambient trucks. This study focused on five-axle trucks traveling thesouth-lane of the bridge. Strain time history data was used to calibrate finite element models accordingto two scenarios: known and unknown truck characteristic selections. These truck characteristics identi-fied from Weight-In-Motion (WIM) data obtained from Iowa state highways were used in the model cal-ibration. The calibrated models, along with standard HS-20 trucks following AASHTO Load Factor Rating(LFR) method, were used to calculate a set of load ratings for each strain set as per the scenarios. Multipleload rating distributions created for strain sets were combined into a single holistic distribution. For theproposed protocol verification, the distribution was compared to that obtained from a rating package cur-rently used by the Iowa Department of Transportation (Iowa DOT). The resulting distribution sets hadmeans of 1.36 and 1.41 for known and unknown truck selections, respectively and subsequently were24% and 27% greater than those values obtained from the Iowa DOT rating package. The distributioncan be used not only to statistically evaluate structural capacity of such bridges, but also provide essentialinformation for assigning retrofit prioritization of such bridges.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Load ratings are essential for ensuring public safety and makingdecisions regarding funding allocation for US highway bridgemaintenance. Load ratings most commonly come in two forms:inventory and operating. The inventory rating is defined as the liveload that can safely utilize the bridge for an indefinite period oftime while the operating rating is the maximum permissible liveload that can be placed on the bridge for the vehicle used in the rat-ing [1]. These load ratings, which are included in the NationalBridge Inventory (NBI), are calculated according to the AASHTOManuals [1,2]; in this work the Load Factor Rating (LFR) methodhas been used [1]. Federal funds for bridge management are allo-cated to Departments of Transportation (DOTs) based upon the suf-ficiency rating, which is computed with information in the NBIdatabase [3]. In addition to funding allocation, load rating, a criticalquantity for the determination of structural capacity, is commonlyused for making decisions regarding bridge repair, rehabilitation,and replacement.

Field testing with known loadings has historically been used todetermine the load-carrying capacity of existing bridges in the Uni-ted States [4–11] according to AASHTO Manuals [1,2]. These man-uals [1,2] give guidelines for evaluating the structural capacity ofexisting bridges through the use of experimental and analyticalload rating data. In addition to the AASHTO Manuals, the structuralcapacity for bridges on European road networks has been assessedusing field measurements [12–14] based on their individual coun-try codes, such as the United Kingdom Design Manual for Roadsand Bridges (DMRBs). The DMRB [15] provides formal proceduresto determine load-carry capacity that is derived from the relation-ships between load and resistance effects although current EURO-CODES [16] which focus on formal bridge design guidelines haveno standard load rating manuals [17]. For critical bridges in theUnited States and Europe, field tests using trucks with bridge clo-sure are often performed to substantiate actual bridge behaviorand to calibrate finite element models used in structural integrityassessments. However, American and European bridge engineersraised concerns about the models’ calibration with single point intime measurements [17]. For more reliable and efficient in-servicestructural capacity assessment, the models should be refined withcontinuously collected field data.

Fig. 1. Statistical estimate of load rating of existing bridges using SHM system.

570 J. Seo et al. / Engineering Structures 46 (2013) 569–580

The manual-based field tests can be conducted to unquestion-ably investigate actual bridge behavior and evaluate its capacity.Hence, the field tests can decrease uncertainties associated withthe load and resistance effects, and increase its reliability for moreaccurate structural assessment of bridges. When determining field-based ratings, the ratings are only calculated using limited data ob-tained from infrequent field tests. The relatively high cost and ef-forts associated with performing the tests compared to analyticalsimulations and the fact that the tests are often executed at a con-siderable distance from bridge owners’ office inhibit a more fre-quent testing regimen. Therefore, analytical models calibratedwith limited field data are frequently used for structural safetyassessments of bridges under different loading types [13–15,18].These field data are typically collected and evaluated via a struc-tural health monitoring (SHM) system with various sensors [19–23]. Though current SHM systems are capable of continuouslymonitoring and collecting real-time bridge responses with no traf-fic control, these systems have not been fully integrated into loadrating frameworks that are able to evaluate the structural ade-quacy of bridges for consecutive periods. Because past studies usedtrucks with known weights and configurations for testing [4–10],those studies have not needed to take into account ambient truckparameters, such as gross vehicle weights (GVWs), transverse loca-tions, and configurations. When appraising structural capacity ofbridges with ambient data, uncertainties in these parametersshould be considered in the rating algorithms since these parame-ters significantly affect bridge responses.

The aim of this paper is to describe a proposed protocol using astrain-based SHM that captures actual bridge response to unknowntrucks, and its application to assess the structural integrity of in-service bridges based upon statistical load rating distributions.The emphasis of this paper is to use finite element models cali-brated using ambient data collected via the SHM system for moreaccurate and efficient bridge capacity assessment. To demonstratethe protocol, several sets of load rating distributions for a steel I-gir-der bridge were generated. A bridge located in Iowa on US Highway30 was used for this work. Critical locations were instrumentedusing strain sensors to monitor the real-time strain time historydata resulting from the passage of ambient heavy trucks. The straindata were used to calibrate bridge models developed in finite ele-ment software. Truck characteristics were then assumed basedupon Weight-In-Motion (WIM) data obtained from Iowa state high-ways. The characteristics, classified in terms of truck weights andconfigurations that are comparable to the features seen in EuropeanWIM data [24], were used as input loadings during calibration. Thecalibrated models were then used to calculate multiple sets of loadratings using the AASHTO LFR method [1]. In order to substantiatethe protocol that was developed, the sets were compared to a singlerating computed from current Iowa DOT software. The implemen-tation of this protocol may refine existing rating calculation toolsand has the potential to assist with statistical bridge capabilityassessment that aids in repair, replacement, and retrofit.

2. Load rating protocol

The protocol used to estimate bridge load ratings in a statisticalmanner is herein outlined. A flowchart of the in-depth procedure,including the selection of ambient truck-induced strain data col-lected through a SHM system, analytical model calibration and sta-tistical bridge capability estimation, is shown in Fig. 1. The firststep is to randomly select sets of actual strain data from the targetbridge loaded by ambient trucks. Damage-sensitive and other glo-bal response locations were instrumented using strain sensors[23]. The feasibility of strain data collection, reduction and evalua-tion was demonstrated in previous work [23].

The second step which focuses on model calibration with ambi-ent strain data has two critical sub-steps: model calibration andrating calculation. Two possible scenarios were tried for the firstsub-step: (1) known and (2) unknown truck characteristic selec-tions. In the first scenario, ambient truck characteristics were iden-tified by investigating strain time history patterns obtained fromthe deck bottom sensors. These patterns allowed for the identifica-tion of ambient truck configurations, including axle numbers andspacings. WIM trucks that closely match the features were identi-fied and then used for model calibration. For the second scenario,to account for more variability in the configurations rather thanthe first scenario, a number of unknown trucks were randomly se-lected from the WIM inventory and then used to calibrate the mod-els. In both scenarios, the WIM data were obtained from weighstations located near the target bridge. The scenarios are describedin greater detail in the next section.

For both scenarios, the models were generated using WinGensoftware – a finite element software package developed by BridgeDiagnostics Inc. (BDI) [25]. WinGen enables bridge engineers to de-fine all aspects of a planar-level model. Model properties consid-ered critical to model calibration included moments of inertia forsignificant components, moduli of elasticity for materials, and rota-tional restraints at the supports. In this work, initial values were de-fined for the calibration parameters based on geometric andmaterial information from a review of the as-built bridge plans.Ranges over which the parameters could be varied were also setbased upon engineering judgment after reviewing conditions ob-tained from inspection. When bridge plans are unavailable, the ini-tial values may be defined based on nominal material propertiesand field measured geometries. Each developed model was individ-ually loaded by each truck in both scenarios, and then was cali-brated such that the bridge response closely matched themeasured strain response. The calibration process required multi-ple iterations and least squares regression analysis to minimize sta-tistical errors between field and analytical responses. These errors,including Percent Error (PE), Percent Scale Error (PSE), and Correla-tion Coefficient (CC), are showed in the following equations [25]:

PE ¼ 100 �Pðef � eaÞ2Pðef Þ2

!ð1Þ

PSE ¼ 100 �P

max jef � eajPmax jef j

� �ð2Þ

J. Seo et al. / Engineering Structures 46 (2013) 569–580 571

CC ¼Pðef � ef Þðea � eaÞP ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðef � ef Þ2ðea � eaÞ2

q0B@

1CA ð3Þ

where ef and ea stand for the field and analytical strain responses;and ef and ea are the sample means of ef and ea respectively. Theprocess was completed when the errors were minimized by incre-mentally adjusting the parameters within their plausible ranges.In addition to the statistical process, a visual comparison of the ana-lytical and field responses was conducted to ensure that the modelswere capable of replicating actual responses.

The second sub-step of the protocol is the load rating calcula-tion using the calibrated models. The ratings were separately com-puted for known and unknown truck scenarios. According to theAASHTO Manual [26], the ratings are computed as follows:

RF ¼ C � cDL � DLcLL � LL � ð1þ IÞ

� �ð4Þ

in which RF stands for the rating factor; C, DL, and LL denote thebridge capacity, dead load effect, and live load effect, respectively;cDL is the dead load factor; cLL is the live load factor; and I is the dy-namic impact factor. Note that cDL and cLL are 1.30 for operatingload rating, while cDL and cLL are 1.30 and 2.17 for inventory loadrating, respectively. The capacity of critical sections was calculatedbased upon AASHTO LFR methods [26]. The dead and live load ef-fects were computed using the calibrated models. To reduce theinfluence of distinctive truck configurations, multiple sets of straintime history data were considered. The load rating procedure incor-porating the models calibrated for each selection scenario was re-peated for many sets of strain data. Multi-load rating distributionswere created for critical bridge components such as girders.

The final step is to combine multiple rating distributions into asingle distribution for each of the considered scenarios, in order toassess the structural adequacy of the selected bridge. The singledistribution accounting for the variability in the ambient truckcharacteristics allows for the evaluation of bridge adequacy in amore reliable fashion.

3. Protocol application

The primary objective of this section is to demonstrate theapplication and capability of the proposed protocol to evaluateAASHTO LFR-based structural capacity for an existing bridge undernormal truck traffic whose behavior was captured from a SHM sys-tem. Information given below includes the bridge description, eval-uation of ambient truck-induced strain data, identification of WIMtruck features, and details of the models used to calculate multiplesets of load rating distributions for known and unknown trucks.

3.1. Bridge description

A composite steel–concrete bridge on US Highway 30 in Iowawas selected to demonstrate the proposed protocol. The US 30bridge consisting of two travel lanes has three spans with twoequal outer spans of 29.7 m and a longer middle span of 38.1 m.The bridge is 9.1 m wide and is skewed 20� right ahead. The overallbridge geometry and typical cross-section with sensor locationscan be seen in Fig. 2. The superstructure consists of two continuouswelded steel plate girders, floor beams, and two stringers that sup-port a 0.184 m thick, cast-in-place concrete deck. A pinned typeconnection exists at the west pier, while roller type connectionsexist at the east pier and each abutment. The abutments are stubreinforced concrete, and the piers are monolithic concrete [27].Photographs of the bridge can be seen in Fig. 3.

3.2. Strain time history responses

Strain data created by ambient trucks were collected using theSHM system installed on the bridge in an earlier study [23]. The fo-cus of the system was to monitor and detect damage in the bridgeby investigating the change in response based upon statistical the-ories [27]. A total of 40 superstructure locations (i.e., top flange,web, and bottom flange of girders) were monitored using fiber op-tic strain sensors. Also, eight sensors were installed on the deckbottom for the purpose of estimating several important truckparameters. The multiple girder sensors enabled the system to cap-ture the local and global bridge system response to ambient trucks.The network of deck bottom sensors allowed for the identificationof axle number, transverse position, and axle spacing. Each axle ofambient trucks yielded a distinctive peak point for a single deckbottom sensor so that corresponding strains were used to identifyambient truck characteristics.

Multiple sets of strain data from the bottom flange of girderswere used in the developed protocol to reduce the influence causedby differences in the truck features. The five data sets utilized here-in were extracted from the strain transducers when five differentambient trucks crossed the bridge. The strain changes influencedby environmental variances (e.g., temperatures) were removedfrom the data through the three step data preprocessing algorithmincorporated in the SHM system [27]. Therefore, the filtered straindata were ultimately used for this study. More details on the algo-rithm can be found in the past work [27].

The five data sets from the girder bottom flange gauges on thenorth and south girders at sections B and D are plotted in Fig. 4.As expected from the fact that the trucks traveled the south-laneof the bridge, the magnitude of strain peaks and overall strain re-sponses at the bottom flange of the south girder appeared to be lar-ger than that of the north girders. The remaining data were alsoconsistent with the relationship between trucks and sensor loca-tions. The truck configurations were identified from deck bottomsensor data. Fig. 5 illustrates the strain time history sets for deckbottom sensor line 1 and 2 (Fig. 2). Peak strain patterns in the fig-ures can be interpreted to indicate the truck type along with axlenumbers. Fig. 5a–c and e indicate four semi-trucks having five-axles for strain sets 1, 2, 3 and 5, respectively. On the other hand,one dump truck with five-axles for strain set 4 is identified fromFig. 5d. For a better understanding of the truck configurations,spacings between the truck axles were calculated from each figureand truck speed. Their speeds were first calculated as the distancebetween the two deck sensor lines over the time duration that eachtruck traveled from the deck line 1–2. The spacing between eachaxle was then determined by multiplying the speed and the traveltime. Table 1 summarizes the calculated axle spacings for the fivetrucks. As indicated in this table, the dump truck for strain set 4 hasrelatively equal spacings for the second, third, and fourth spacingas opposed to that of the semi-trucks.

3.3. Ambient truck inventory

It is well known that traffic includes trucks with various config-urations, weights, and travel paths. As trucks cross a bridge, numer-ous combinations of individual parameters lead to different bridgeresponses. To treat the uncertainty in the unknown trucks, a largenumber of ambient five-axle trucks with different axle weightsand spacings were used in the model calibration process resultingin a similarly large number of bridge models. The ambient truckinventory was obtained from Dallas and Jasper County weigh sta-tions located in Iowa. The weigh station data had been recordedover two consecutive years from 2009 to 2011. During this period,175,343 trucks classified as five-axle trucks were recorded. Statisti-cal distributions from the five-axle trucks were created to explicitly

(b)

(a)

Fig. 2. US30 bridge schematic: (a) 3D frame plan; (b) typical cross-section with sensor locations.

Fig. 3. Photographs of US30 bridge [27]: (a) side view; (b) bottom view.

572 J. Seo et al. / Engineering Structures 46 (2013) 569–580

explore ambient truck characteristics. The spacing between axles 1and 2 (i.e., the first spacing), the spacing between axles 2 and 3 (i.e.,the second spacing), the spacing between axles 3 and 4 (i.e., thethird spacing), the spacing between axles 4 and 5 (i.e., the fourth

spacing), and the GVW, are shown in Fig. 6. These figures indicatethat the first, second, third and fourth spacing are most frequently5.2 m, 1.2 m, 10.2 m, and 1.2 m, respectively. A significant range ofthe first and third spacing and GVW can be seen in the figures. How-

Fig. 4. Five strain sets at bottom flange of: (a) north girder at section B; (b) south girder at section B; (c) north girder at section D; (d) south girder at section D.

J. Seo et al. / Engineering Structures 46 (2013) 569–580 573

ever, there is an insignificant range of variation in the second andfourth spacing as shown in the figures. It can be interpreted thatfive-axle semi-trucks most commonly occur. The WIM data wereused as vehicular input loads in the model calibration processwhich is discussed in more depth in the following section.

3.4. Model generation and calibration

A planar-level finite element model of the US30 bridge includ-ing transverse deck elements was generated using 747 linear beamelements, 522 quadrilateral shell elements and four rotationalspring elements in WinGen [25]. The shell elements were primarilyused to model the transverse distribution of vertical live loads tothe girders. As can be seen in Fig. 7, the girders, stringers and floorbeams were modeled with elastic beam elements, whereas theconcrete deck was idealized with quadrilateral shell elements. Inpast work [27], experimental data indicated that both the girdersand stringers behave compositely with the concrete deck; thus,all steel girder and stringer sections were modeled as compositebeams. Initial section and material properties were assigned toall elements based upon the bridge plan prior to model calibration.The boundary conditions were also idealized using rotationalspring elements with appropriate initial stiffness.

The calibration process was accomplished based upon bothknown and unknown truck characteristic selection scenarios usingthe generated model. In the former, WIM trucks most identical tothe measured truck characteristics were used, while in the lattera large number of trucks randomly selected from WIM data wereused. In each case the uncertainty in ambient truck parameterscan be minimized by performing a large number of finite elementmodel simulations covering different load patterns. The scenariosare further detailed in the following subsections.

3.4.1. Known truck characteristic selectionOnce the truck axle spacings were determined from the deck

bottom sensors, the data from Fig. 5 and Table 1 were utilized to

find trucks of similar geometry from the WIM inventory. In strainset 1, for example, the first, second, third, and fourth spacings are4.6 m, 1.3 m, 7.9 m, and 2.4 m, respectively. Only four trucks thatclosely matched these spacings were identified in the WIM data.The same selection procedure was followed for the other axle spac-ings. Table 2 lists the selected WIM truck characteristics for eachset. In total, 15 trucks were selected. These trucks were then usedin the model calibration.

Critical calibration parameters were defined to be the momentsof inertia for the main girders, stringers, and floor beams; modulusof elasticity for the concrete deck; and rotational restraints at theabutments. The initial values were determined via a review of thebridge plans and limits set based upon engineering judgmentregarding the condition of the bridge. Individual WIM trucks foreach set were applied to the model and corresponding strain re-sponses were obtained. The responses were used as the basis forcalibrating the model in WinSac, part of the standard BDI softwarepackage [28]. The model was refined by minimizing the PE, PSE, andCC errors between the analytical and measured strain responses. Tominimize the errors, incremental changes of the parameters weremade to the model within the predetermined bounds. Repetitionof this process with different trucks in conjunction with variabilityin transverse locations produced 500 calibrated models, whichwere then used to generate rating distributions. Table 3 showsthe statistics of the structural properties for the parameters ad-justed using known trucks. As listed in Table 4 for all sets, the modelaccuracy is reported in terms of Mean PE, Mean PSE and Mean CCalong with their standard deviations. This table indicates that thesesets have good correlation with the measurements.

3.4.2. Unknown truck characteristic selectionWhere the trucks were assumed to be completely unknown,

500 trucks were randomly selected from the WIM data recordsand used as input loads for model calibration. The models incorpo-rating the unknown trucks were also generated with WinSac [28].

Fig. 5. Five truck-induced deck-bottom strains for deck line 1 and 2: (a) strain 1; (b) strain 2 (c) strain 3; (d) strain 4; (e) strain 5.

Table 1Speed and axle spacing for selected five trucks with five-axles, highlighting inboldface the values for the dump truck.

Data sets Speed (km/h) Axle spacing (m)

S1 S2 S3 S4

Strain 1 98.6 4.6 1.3 7.9 2.4Strain 2 85.7 4.2 1.5 10.8 1.1Strain 3 98.3 5.0 1.3 8.3 1.3Strain 4 92.2 3.3 1.0 1.2 1.0Strain 5 92.5 5.7 1.2 10.9 3.1

Note: S1, S2, S3, and S4 denote the first, second, third, and fourth spacing,respectively.

574 J. Seo et al. / Engineering Structures 46 (2013) 569–580

A single truck was applied to the model, and then the structuralproperties of the considered parameters such as moment of inertia

were optimized by minimizing the PE, PSE, and CC errors followingthe aforementioned process. Table 3 provides a statistical sum-mary of the parameter values calibrated with unknown trucks. Ta-ble 4 summarizes the model accuracy for all sets. Aside from thestrain 4 models, the remaining model sets had good correlationwith the field data. It is assumed the variance in set 4 occurred be-cause a five-axle dump truck induced the response, while mosttrucks in the WIM database are not dump trucks. The other setsmodels were calibrated with the actual responses resulting fromfive-axle semi-trucks.

In addition to a statistical evaluation, the graphical accuracywas evaluated as shown in Fig. 8. For comparison, representativeplots between the measured and analytical data at different sen-sors are given, where Fig. 8a and b illustrate typical strains at thenorth girder of section B and D and Fig. 8c and d illustrate thoseat the south girder of section B and D. From these and other similar

Fig. 6. Statistical distributions of ambient five-axle truck inventory: (a) spacing of axle 1 and 2; (b) spacing of axle 2 and 3; (c) spacing of axle 3 and 4; (d) spacing of axle 4 and5; (e) gross truck weight.

Fig. 7. Analytical model of US 30 Bridge.

J. Seo et al. / Engineering Structures 46 (2013) 569–580 575

comparisons, it was concluded that the models reasonably repre-sented the measured response over most points, though slight dif-ferences between the actual and analytical strains in some pointsoccurred.

3.5. Ambient bridge rating generation

Rating models, incorporating AASHTO HS-20 trucks and bridgeself-weight, were generated using the created models. Included

in the self-weight were the steel girders, stringers, floor beamsand concrete deck. As the bridge was designed for two lanes, truckpath envelopes were generated for two trucks on the bridge at thesame time. Regarding multi-truck positioning, AASHTO [26] stipu-lates that the transverse distance between two trucks should be1.22 m. Hence, the two trucks were placed side-by-side at 0.61 mand 3.66 m from the south curb as shown in Fig. 9. Following therequirements of AASHTO [26], negative and positive flexural capac-ities, which were used as the basis for the rating calculation, were

Table 2WIM trucks specific to the trucks detected via SHM system.

Data sets WIM trucks Axle spacing (m) GVW (kN)

S1 S2 S3 S4

Strain 1 Truck A 4.6 1.3 8.8 2.6 281.1Truck B 4.6 1.3 8.8 2.6 285.6Truck C 4.6 1.3 8.7 2.8 247.2Truck D 4.6 1.3 7.5 2.8 249.3

Strain 2 Truck E 4.2 1.3 10.9 1.2 163.0Truck F 4.2 1.3 10.9 1.2 185.6Truck G 4.2 1.3 10.9 1.2 222.8

Strain 3 Truck H 5.1 1.3 8.4 1.2 344.7Truck I 5.1 1.3 8.4 1.3 330.6Truck J 5.1 1.3 8.4 1.2 212.0

Strain 4 Truck K 3.3 1.1 1.2 1.3 192.1Truck L 3.3 1.1 1.3 1.3 282.1Truck M 3.3 1.1 1.3 1.3 286.3

Strain 5 Truck N 5.7 1.3 10.8 3.1 144.3Truck O 5.7 1.3 10.8 3.1 315.4

Note: S1, S2, S3, and S4 are the first, second, third, and fourth spacings, respectively.

Table 3Calibration parameters for known and unknown truck selection scenarios.

Scenarios Sets Statistics

Girder at spans, Iy

(cm4)Girder near piers, Iy

(cm4)Stringer, Iy (cm4) Floor beam, Iy (cm4) Concrete deck, E

(MPa)Rotational spring, kr

(cm-kN/rad)

Mean,l

Standarddeviation, r

Mean,l

Standarddeviation, r

Mean,l

Standarddeviation, r

Mean,l

Standarddeviation, r

Mean,l

Standarddeviation, r

Mean, l Standarddeviation, r

Knowntruck

Strain 1 3.7E+06 9.2E+05 8.7E+06 1.2E+06 5.5E+05 1.2E+06 2.8E+05 2.8E+05 1.8E+04 3.7E+03 1.1E�04 2.6E�04Strain 2 4.2E+06 9.9E+05 9.3E+06 7.2E+05 7.1E+05 8.5E+05 5.7E+04 5.4E+04 2.9E+04 5.4E+03 3.0E�03 4.0E�03Strain 3 4.3E+06 8.6E+05 9.4E+06 4.2E+05 9.7E+05 1.9E+06 1.0E+05 2.0E+05 2.6E+04 7.0E+03 4.7E�04 9.1E�04Strain 4 3.9E+06 1.0E+06 8.8E+06 1.3E+06 1.7E+06 3.8E+06 2.6E+04 3.1E+04 2.6E+04 6.9E+03 4.1E�04 7.0E�04Strain 5 3.4E+06 8.2E+05 9.2E+06 6.8E+05 4.6E+05 1.9E+05 2.3E+04 3.5E+04 3.4E+04 1.1E+03 5.0E�04 1.1E�03

Unknowntruck

Strain 1 4.2E+06 3.7E+05 9.4E+06 1.2E+05 4.8E+05 9.5E+05 2.5E+05 1.8E+05 1.8E+04 3.3E+03 4.7E�05 5.3E�05Strain 2 3.0E+06 4.4E+05 8.5E+06 8.9E+05 5.9E+05 3.6E+05 8.0E+03 7.7E+03 3.0E+04 6.7E+03 1.4E�04 1.9E�04Strain 3 4.4E+06 5.8E+05 9.1E+06 4.2E+05 3.0E+05 1.9E+05 5.8E+05 6.3E+05 1.7E+04 5.6E+02 1.3E�04 2.1E�04Strain 4 4.5E+06 6.8E+05 9.4E+06 3.7E+05 8.0E+05 3.9E+05 1.8E+04 4.3E+04 3.2E+04 5.0E+03 9.8E�04 1.9E�03Strain 5 3.3E+06 7.4E+05 9.2E+06 3.4E+05 1.7E+06 5.7E+06 3.2E+04 6.8E+04 3.3E+04 4.1E+03 6.4E�04 1.1E�03

576 J. Seo et al. / Engineering Structures 46 (2013) 569–580

computed at all locations. The inventory load ratings for the gird-ers, the major components resisting vertical loads, were calculatedat all locations using the AASHTO capacities [26]. The lowest rat-ings extracted during the analyses were used to generate the rat-ings for each scenario.

3.5.1. Ratings for known trucksThe 500 models calibrated for each strain set with known truck

characteristics and different transverse truck positions were usedto perform load ratings. Five-hundred ratings for each set were cre-ated for the girder as shown in Fig. 10. All distributions appear tobe asymmetric. Distributions for set 1, 2, and 3 have sharp peaksand longer-left-side tails while distributions for set 4 and 5 havelonger-right-side tails with sharp peaks. For better interpretationof these distributions, the statistical characteristics were alsoexamined as listed in Table 5. Mean rating values ranging from1.29 to 1.47 were computed over all sets. For comparison betweenthe sets with different means, coefficients of variation were calcu-lated, showing that there was insignificant difference. As expectedfrom the distribution shapes, the table indicates that set 1, 2, and 3have positive skewness and kurtosis coefficients indicating that thebulk of the data points lie to the left of the mean and sharp peaks,whereas set 4 and 5 have negative skewness and kurtosiscoefficients.

The five rating distributions were combined into a single distri-bution including 2500 ratings. The process to create the holisticdistribution was as follows: (1) a range on the abscissa sufficientto cover the largest and smallest ratings was selected, and thisrange was divided into intervals to best show the distribution,(2) the number of all ratings for five sets was recounted withineach interval, and (3) a vertical axis with the number of occur-rences within the intervals was plotted. Following this process,the holistic distribution was constructed for known trucks, andcan be seen in Fig. 11. Structural capacity of the bridge was statis-tically evaluated using the distribution. The distribution has themean of 1.36 with a standard deviation of 0.1. Mode, minimaand maxima are 1.35, 1.10, and 1.70, respectively. Therefore, itcan be interpreted from the statistical bridge ratings for knowntrucks that the load-carrying capacity had on average 36% abovethat required which indicates that the bridge has sufficient flexuralcapacity.

3.5.2. Ratings for unknown trucksThe 500 models calibrated with unknown trucks were subjected

to HS-20 loads to create load rating distributions for each strainset. These ratings were also included in Fig. 10. All distributions,which are explicitly skewed, have sharp peaks and longer and fat-ter tails on the right side than the left. Notably, one distribution,

Table 4Model accuracy for known and unknown truck selection scenarios.

Scenarios Sets Statistics

PE PSE CC

Mean, l (%) Standard deviation, r (%) Mean, l (%) Standard deviation, r (%) Mean, l Standard deviation, r

Known truck Strain 1 6.50 1.78 6.58 0.46 0.97 0.01Strain 2 7.58 1.07 6.37 1.15 0.96 0.01Strain 3 8.58 1.64 7.47 1.16 0.97 0.01Strain 4 13.07 4.59 5.40 1.09 0.95 0.01Strain 5 11.12 5.87 7.34 2.40 0.95 0.02

Unknown truck Strain 1 9.78 3.86 7.02 0.95 0.96 0.01Strain 2 9.11 4.00 6.37 1.16 0.96 0.01Strain 3 8.77 3.66 6.30 0.93 0.96 0.01Strain 4 21.02 9.37 6.53 2.30 0.91 0.03Strain 5 12.99 4.55 13.00 1.92 0.95 0.02

Fig. 8. Representative strain comparison between field tests and analytical models: (a) north girder at section B; (b) north girder at section D; (c) south girder at section B; (d)south girder at section D.

J. Seo et al. / Engineering Structures 46 (2013) 569–580 577

Fig. 10e, has a narrower dispersion pattern over the data points rel-ative to the other distributions. Table 5 also shows the statisticalcharacteristics for unknown trucks. This table indicates mean val-ues varying from 1.26 to 1.54 were observed from the sets andthere was no substantial difference in coefficients of variationthough strain 4 does seem to stand out. All distribution patternsare in good agreement with the skewness and kurtosis coefficients,representing that the majority of the data points lie to the left ofthe mean and the distribution has sharp peaks.

A holistic distribution that covers 2500 ratings was generatedfor unknown trucks following the process specified previously.

Fig. 11 also includes the ratings. The distribution was used to sta-tistically evaluate structural capacity of the bridge. The distribu-tion has the mean of 1.41 with a standard deviation of 0.25.Mode, minima and maxima are 1.35, 1.05 and 3.29, respectively.Similar to the findings from the ratings for known trucks, the meanstructural capacity of the bridge was 41% beyond that required.However, it should be noted that the holistic ratings were widelydistributed relative to those from the known truck calibrationmethod. The difference between the two sets of distributions canbe attributed to the level of variability in truck weights andspacings.

Fig. 9. Transverse position of AASHTO standard HS-20 Trucks on US 30 bridge.

Fig. 10. Load rating distribution sets for: (a) strain 1;

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4. Rating comparison

To verify the protocol, the two sets of the holistic distributionswere compared against a rating determined from the Iowa DOT.The lowest girder rating was 1.03 as also shown in Fig. 11. This va-lue was 24% and 27% lower than the mean from the known and un-known truck ratings, respectively. Differences between the resultsoccurred because of three main factors: (1) Modeling approach –The protocol used the planar-level model to represent transversetruck positions, but the Iowa DOT software package used singleline girder method not capable of modeling enhanced lateral loaddistribution effects; (2) Actual response of the bridge – The model

(b) strain 2; (c) strain 3; (d) strain 4; (e) strain 5.

Table 5US 30 Bridge rating distribution characteristics for known and unknown trucks.

Scenarios Distributions Statistics

Mean, l Standard deviation, r Coefficient of variation, cm Skewness coefficient, cs Kurtosis coefficient, ck

Known truck Strain 1 1.35 0.05 0.04 1.13 1.47Strain 2 1.30 0.06 0.05 1.11 1.88Strain 3 1.39 0.06 0.05 0.31 2.14Strain 4 1.47 0.10 0.07 �1.12 �0.01Strain 5 1.29 0.09 0.07 �0.13 �1.38

Unknown truck Strain 1 1.38 0.23 0.16 3.85 20.04Strain 2 1.42 0.16 0.12 0.48 1.47Strain 3 1.47 0.26 0.17 2.69 9.59Strain 4 1.54 0.33 0.21 2.09 4.85Strain 5 1.26 0.1 0.08 2.12 16.77

Fig. 11. Holistic load rating distribution compared to single rating obtained fromIowa DOT package.

J. Seo et al. / Engineering Structures 46 (2013) 569–580 579

in the protocol was calibrated with various strain data to predictactual behavior of the bridge, while the Iowa DOT software didnot; (3) Ambient truck effect – A large number of ambient truck-in-duced simulations were used in the protocol to account for uncer-tainty in their characteristics, whereas the DOT package did nottake into account these effects in the calibration process. Therefore,it is anticipated that the protocol can be used for more reliable esti-mate of the structural capacities of in-service bridges rather thanthe current approaches.

5. Summary and conclusions

The load rating protocol in conjunction with a SHM system wasdemonstrated for the generation of multiple rating distributionsfor the statistical assessment of the structural integrity of steel I-girder bridges subjected to common heavy trucks. A bridge locatedin Iowa and ambient truck characteristics identified using WIMdata obtained from the Iowa DOT were selected for this study.The SHM system was employed to monitor, collect, and evaluatereal-time strain data of the bridge under ambient five-axle trucks.Finite element models were generated using different types ofstructural elements, and calibrated using WIM trucks based upontwo scenarios: known and unknown truck characteristic selectionscenarios. The models loaded by known and unknown trucks fromthe WIM pool were calibrated; these models had correlation coef-ficients of greater than 0.9. The models incorporating HS-20 truckswere used to calculate the rating distributions for both scenarios.To account for the large variation in the ambient trucks over time,the multi-distribution sets were combined into one holistic

distribution for each scenario. Significant results from multipleand holistic distributions are summarized as follows:

� Multiple distributions that were computed for known andunknown trucks were asymmetric. On average ratings forknown trucks were ranged from 1.29 to 1.47, whereas thosefrom unknown trucks varied from 1.26 to 1.54 although thetwo sets of rating distributions showed that there was insignif-icant difference in coefficients of variation. Most distributionshad positive skewness and kurtosis coefficients, indicating themost points lie to the left of the mean with sharp peaks.� Holistic distribution for known trucks had a mean of 1.36 with a

standard deviation of 0.01, while unknown truck-induced dis-tribution had the mean of 1.41 with the standard deviation of0.25. As anticipated, the distribution for unknown trucks hada wider range of ratings relative to the distribution obtainedfrom known truck selection scenario. The difference betweenthe two distributions was due to the variability in the truckcharacteristics.� Comparison between ratings from the proposed protocol and

Iowa DOT software showed that the means observed fromknown and unknown truck-induced distributions are 24% and27% larger than the Iowa DOT. The generic dissimilaritybetween the results occurred due to modeling approach, useof actual response, and uncertainty in ambient trucks.

This study offered insight into the statistically evaluated ade-quacy of an existing bridge and into ambient truck variances thatcould significantly impact its capacity. Hence, the implementationof this protocol may improve current load rating approaches tobetter estimate the structural capacity of these bridges. This proto-col can also become an essential tool for aiding maintenance andrepair decisions. Beyond the limited application to these bridgetypes, in future work, the protocol can be extended to differenttypes of bridges, including suspension and cable-stayed bridges.The protocol can be also incorporated with fragility curve deriva-tion algorithms to evaluate ambient truck-induced vulnerabilityof bridges. These curves can be used to calculate exceedance prob-abilities over a varying range of truck weights, configurations,speeds, positions, and bridge conditions. In addition to the fragilityanalysis, the protocol incorporating time-variant models for bothlive load increase and resistance deterioration is able to evaluatetime-dependent bridge capability.

Acknowledgments

The authors acknowledge the support of this work via a pooledfund project administered by the Iowa DOT. Other study partici-pants include CALTRANS, Illinois DOT, the USDA Forest ProductsLaboratory, and the Federal Highway Administration.

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